Managing more than the mean: using quantile regression to identify factors related to large elk groups

Animal group size distributions are often right-skewed, whereby most groups are small, but most individuals occur in larger groups that may also disproportionately affect ecology and policy. In this case, examining covariates associated with upper quantiles of the group size distribution could facilitate better understanding and management of large animal groups. We studied wintering elk groups in Wyoming, where group sizes span several orders of magnitude, and issues of disease, predation and property damage are affected by larger group sizes. We used quantile regression to evaluate relationships between the group size distribution and variables of land use, habitat, elk density and wolf abundance to identify conditions important to larger elk groups. We recorded 1263 groups ranging from 1 to 1952 elk and found that across all quantiles of group size, group sizes were larger in open habitat and on private land, but the largest effect occurred between irrigated and non-irrigated land [e.g. the 90th quantile group size increased by 135 elk (95% CI=42, 227) on irrigation]. Only upper quantile group sizes were positively related to broad-scale measures of elk density and wolf abundance. For wolf abundance, this effect was greater on elk groups found in open habitats and private land than those in closed habitats or public land. If we had limited our analysis to mean or median group sizes, we would not have detected these effects.Synthesis and applications. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management. Our analysis of elk group size distributions using quantile regression suggests that private land, irrigation, open habitat, elk density and wolf abundance can affect large elk group sizes. Thus, to manage larger groups by removal or dispersal of individuals, we recommend incentivizing hunting on private land (particularly if irrigated) during the regular and late hunting seasons, promoting tolerance of wolves on private land (if elk aggregate in these areas to avoid wolves) and creating more winter range and varied habitats. Relationships to the variables of interest also differed by quantile, highlighting the importance of using quantile regression to examine response variables more completely to uncover relationships important to conservation and management.